Kantorovich: Mathematics Applied to Economics
Special to The St. Petersburg Times
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For The St. Petersburg Times
King Carl XVI Gustaf of Sweden presenting Leonid Kantorovich with his Nobel Prize for Economics on Dec. 10 1975.
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Leonid Kantorovich, the St. Petersburg scientist who was awarded a Nobel Prize in 1975, bridged the theoretical world of mathematics and the practical world of economics, research that sometimes put him at odds with the Soviet state. The methods he developed were universal - useful not only in a planned economy such as the one he lived in, but also in capitalist countries where free markets operated. When Kantorovich was presented with his Nobel Prize for Economics, the Swedish Royal Academy's Professor Ragnar Bentzel emphasized the importance of Kantorovich's scientific work for the world's economy. "The basic economic problems are the same in all societies, regardless of whether these are characterized by capitalism, socialism or other types of political organization," Bentzel said. Kantorovich was already a professor at the age of 20, a member of the Soviet Academy of Sciences at the age of 52 and a Nobel Prize winner at 63. He invented linear-programming and is considered the father of Russian econometrics - the application of mathematics and statistics to economic problems. Born in 1912 in what was then St. Petersburg, Kantorovich died in 1986, in what was still Leningrad. His father, a doctor, died when Leonid was only 10 years old, leaving his mother, Paulina, to raise him alone. Leonid was almost an infant prodigy with a broad range of interests, including politics and modern history. While still in school, he received scholarship for gifted children and he was only 14 when he enrolled in the mathematics department of the Leningrad State University. He said later that this was "the very time when his first interest in sciences and the first displays of self-dependent thinking manifested themselves." He quickly established himself as an authority on mathematics, even among his much older classmates. One of them was Solomon Michlin, who would go on to become a professor and member of two foreign Academies of Sciences. In his memoirs he described the Kantorovich of those days: "I remember my first vivid impression of Leonid - a bit shortish with blushing cheeks. He was very much like a boy. I could not understand what this small boy was doing at the university. I was quite grown-up, almost 20 years old, while he was only 14. I remember how astounded we were less than a year later when Leonid's first works were published. For us third-year students it seemed incredible and impossible." Leonid soon became well known among Leningrad and Moscow mathematicians for his research on abstract mathematics. After he graduated at age 18, he decided to stay on and continue his research, combining it with teaching. He lectured at the Institute of Industrial Construction Engineering and in two years Kantorovich became a professor at the institute. After another two years, he became a professor at his alma mater. One of his students Sergei Chesnokov, later a professor at the Higher School of Economics in Moscow, would later write: "When Leonid Vitalyevich [Kantorovich] came to his first lecture a couple of students shouted at him: "Hey, you, you'd better take your seat, the professor is about to come." In 1935, when the system of academic degrees was restored in the Soviet Union, Kantorovich received his doctorate without having to defend a thesis. The focus of his work started to shift from theoretical toward applied mathematics. His most renowned achievements at that stage lay in functional analysis and numerical analysis. He published papers on the theory of functions, the theory of complex variables, descriptive set theory and many other fields of mathematics. But the work that was most fruitful and that he received the most praise for was on partially-ordered spaces. Kantorovich started this research in 1935 and by 1937 was teaching a special course called "Functional analysis based on the theory of partially-ordered spaces." These spaces would eventually be named after the scientist; today they are called Kantorovich-spaces or, briefly, K-spaces. Kantorovich married in 1938 and remained with his wife, Natalya, until his death. They had two children - a daughter and a son, who both later chose careers in mathematical economics. Many of Kantorovich's contemporaries and students emphasize his amazing ability to work on several different problems at a time and organize the activities of many people on the problems. This may be one reason why most of his books were written with a coauthor. In his first book on applied mathematics, "Approximate Methods of Higher Analysis," written together with Vladimir Krylov, Kantorovich outlines the methods of using functional analysis in solving real world applications. This work received major critical acclaim from scholars and was Kantorovich's first step towards integrating theory and application. His second step became even more oriented to practical applications: towards the end of the decade Kantorovich began his first economic research, the field in which he would have his main and most renowned achievements and that would bring him fame and honor. In his autobiography, Kantorovich describes the starting point as accidental. In 1938, he acted as a consultant for the Laboratory of the Plywood Trust. The laboratory wanted to minimize the use of its resources to produce the maximum of goods and services. This piqued Kantorovich's interest in using applying mathematics to economic problems. Economically, the problem was to determine what mix of a limited number of inputs would yield the maximum output. To solve this problem the scientist invented a new type of analysis later called linear programming. The problem he had solved for the Plywood Trust turned out not to be just an occasional and specific one, but one that occurred frequently. Kantorovich found many different economic problems could be resolved using the same mathematical formula. These problems include distribution for workplace equipment, the best use of an area for sowing, finding out how to cut up materials in the most economic way, use of complex resources and distribution of transport flows. New methods of maximizing the output in all those areas eventually found their reflection a brochure "Mathematical Methods of Organizing and Planning Production" (1939). Yet, the conclusions Kantorovich made in this book were met with skepticism. His next paper, "The Best Use of Economic Resources," which developed the use of linear programming for resolving macroeconomic problems, caused even more distrust. In this paper Kantorovich advocated the need to partially decentralize the rigidly planned Soviet economy and showed that even planned economies should consider using prices to allocate resources. His proposals were considered useless and, moreover, "anti-Marxist." It was not published in the Soviet Union until 1959 and it was perhaps only because the Soviet Union was at war that saved Kantorovich from being repressed for the paper. Nevertheless, it was for this paper that he would be awarded the Nobel Prize some 30 years later. The cold shoulder officials and scientists gave to his economic works resulted in Kantorovich shifting his focus back to mathematics. During the war he was a professor at the Higher School for Naval Engineers, and after being evacuated and returning to Leningrad, he advised on calculations that would be used in the development of the Soviet atomic bomb. His mathematical research of that time is summarized in a large article called "Functional Analysis and Applied Mathematics," for which he was awarded the State Prize. It was the final step in connecting theoretical and applied mathematics, an idea that mathematicians and economists once considered contradictory, Kantorovich would later write in his biography. During World War II, Kantorovich also became interested in computation problems, which produced some recommendations on how programming might be automated and also on computer construction. Afterward, as the Soviet Union struggled to recover from a costly and deadly war and mobilized to reconstruct its economy, officials' interest in economics and Kantorovich's work grew substantially. Kantorovich became a corresponding member of the U.S.S.R. Academy of Sciences, was invited to head one of the departments in the Siberian branch of the academy in Novosibirsk and finally in 1959 published his "The Best Use of Economic Resources." The paper caused controversy among Soviet economists and was noticed by western scientists. As a result, Kantorovich's work on linear programming began to be published in Europe and the United States. Kantorovich started to gain recognition all over the world. In 1964, he finally became an academician, received the Lenin Prize, the Soviet Union's top prize, for developing linear programming. He began teaching a special course on economic cybernetics at Leningrad State University and even organized a postgraduate course for specially gifted students. Some factories, including the city's Yegorov subway wagon factory, tried using linear programming in their everyday life. Kantorovich was given honorary doctorates by many European universities, including those in Glasgow, Cambridge, Munich, Nice, and Paris, was made a member of foreign Academies of Sciences and received countless invitations to international conferences on mathematics and econometrics. The Soviet government, however, refused again and again to let him go abroad. Only in 1975, the year he was awarded his Nobel Prize, was Kantorovich allowed to cooperate with foreign academics. Kantorovich shared the prize "for the contributions to the theory for optimal allocation strategies" with American Tjalling Koopmans, who developed linear programming in the 1940s independently of the Russian scholar. Back in Russia with his Nobel Prize, Kantorovich continued to research and promote linear programming methods but now at the Institute of National Economic Planning in Moscow, where he had been working since 1971. All his rewards and degrees notwithstanding, "Leonid Kantorovich was always friendly, understanding and sometimes even timid with his colleagues, friends, students and family" Chesnokov recalled. "Up to the last days of his life Leonid Kantorovich was exuberant and full of plans and productive ideas," his student Semyon Kutateladze says in "L.V. Kantorovich: the man and scientist," a paper he compiled together with Kantorovich's son Vsevolod. Kantorovich even dictated a vast commentary on his life that was eventually issued as a report titled "My Path in Science," which was presented to the Moscow Mathematical Society. He was buried at Novodevichy Cemetery in Moscow, his fundamental input in mathematics and economics having put him among the top scientists of the 20th century. The method of linear-programming he invented was later rediscovered and developed in the works of other scientists - above all by George Danzig. The method is now used to solve problems not only in the field of economics but also in physics, chemistry, geology, biology and many others.
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